Monge-Ampere measures on pluripolar sets
Complex Variables
2008-08-19 v3
Abstract
In this article we solve the complex Monge-Ampere equation for measures with large singular part. This result generalizes classical results by Demailly, Lelong and Lempert a.o., who considered singular parts carried on discrete sets. By using our result we obtain a generalization of Kolodziej's subsolution theorem. More precisely, we prove that if a non-negative Borel measure is dominated by a complex Monge-Ampere measure, then it is a complex Monge-Ampere measure.
Cite
@article{arxiv.0706.0169,
title = {Monge-Ampere measures on pluripolar sets},
author = {Per Ahag and Urban Cegrell and Rafal Czyz and Pham Hoang Hiep},
journal= {arXiv preprint arXiv:0706.0169},
year = {2008}
}